IGCSE Maths Extended Paper 4 (calculator)

Name: ______________________   Date: __________   Marks: ____ / 100

Time: 120 minutes. You may use a calculator. Answer all questions. Show your working. The marks for each part are shown in brackets. steplyclass.com/igcse-maths/extended-paper-4/

1. 1(a) Question 1(a)

   A car costs $18 000. Its value goes down by 15% each year. Find its value after 3 years.

   [3 marks]

   Answer: ____________________

2. 1(b) Question 1(b)

   After a 12% pay rise, Sami earns $33 600 a year. Find his pay before the rise.

   [3 marks]

   Answer: ____________________

3. 1(c) Question 1(c)

   Lena invests $5000 at 3.5% per year compound interest. Find the amount after 6 years.

   [3 marks]

   Answer: ____________________

4. 2 Question 2

   A rectangle measures 12 cm by 7 cm, both correct to the nearest centimetre. Find the upper bound of its area.

   [2 marks]

   Answer: ____________________

5. In triangle ABC, BC = a, AC = b and AB = c.

   3(a) Question 3(a)

   a = 8 cm, b = 11 cm and angle C = 47°. Find c.

   [3 marks]

   Answer: ____________________

6. 3(b) Question 3(b)

   Find the area of the same triangle (a = 8 cm, b = 11 cm, angle C = 47°).

   [2 marks]

   Answer: ____________________

7. 3(c) Question 3(c)

   In another triangle, angle A = 52°, angle B = 71° and a = 9.5 cm. Find b.

   [3 marks]

   Answer: ____________________

8. 4 Question 4

   A ship sails 12 km on a bearing of 065°. How far north and how far east of its start is it?

   [3 marks]

   Answer: ____________________

9. A cuboid measures 5 cm by 8 cm by 6 cm.

   5(a) Question 5(a)

   Find the length of a diagonal from one corner to the opposite corner.

   [2 marks]

   Answer: ____________________

10. 5(b) Question 5(b)

    The cuboid is 5 cm by 8 cm on its base and 6 cm high. Find the angle between the diagonal and the base.

    [3 marks]

    Answer: ____________________

11. 6(a) Question 6(a)

    A sector has radius 9 cm and angle 40°. Find its area.

    [2 marks]

    Answer: ____________________

12. 6(b) Question 6(b)

    A cone has base radius 6 cm and slant height 10 cm. Find its volume.

    [3 marks]

    Answer: ____________________

13. 6(c) Question 6(c)

    A sphere has radius 5 cm. Find its surface area.

    [2 marks]

    Answer: ____________________

14. 6(d) Question 6(d)

    A frustum is made by cutting a small cone (radius 2 cm, height 4 cm) off a large cone (radius 5 cm, height 10 cm). Find the volume of the frustum.

    [3 marks]

    Answer: ____________________

15. 7 Question 7

    Two similar shapes have areas 9 cm² and 25 cm². A length on the small shape is 6 cm. Find the matching length on the large shape.

    [2 marks]

    Answer: ____________________

16. 8 Question 8

    Solve 2x² − 5x − 4 = 0. Give your answers correct to 2 decimal places.

    [4 marks]

    Answer: ____________________

17. 9 Question 9

    Solve the simultaneous equations x² + y² = 25 and y = x + 1.

    [5 marks]

    Answer: ____________________

18. 10 Question 10

    f(x) = x + 4 and g(x) = 2x. Find f(g(x)) and g(f(x)).

    [3 marks]

    Answer: ____________________

19. 11 Question 11

    A town has 12 000 people. The number grows by 2.5% each year. Find the number of people after 4 years.

    [3 marks]

    Answer: ____________________

20. 12 Question 12

    The heights, h cm, of 20 plants: 100 < h ≤ 120: 4, 120 < h ≤ 140: 9, 140 < h ≤ 160: 5, 160 < h ≤ 180: 2. Calculate an estimate of the mean height.

    [4 marks]

    Answer: ____________________

21. 13 Question 13

    Times, t minutes: 0 < t ≤ 10: 2, 10 < t ≤ 20: 6, 20 < t ≤ 30: 10, 30 < t ≤ 40: 2. Use a cumulative frequency table to find an estimate of the median.

    [3 marks]

    Answer: ____________________

22. 14 Question 14

    Two fair dice are rolled. Find the probability that the total is 7.

    [3 marks]

    Answer: ____________________

23. 15 Question 15

    Solve 2 sin x − 1 = 0 for 0° ≤ x ≤ 360°.

    [3 marks]

    Answer: ____________________

24. 16 Question 16

    Triangle P has corners A(2, 1) and B(4, 3). Its image has A'(2, −1) and B'(4, −3). Describe fully the single transformation.

    [2 marks]

    Answer: ____________________

25. 17 Question 17

    Make x the subject of ax + 3 = 2x + c.

    [3 marks]

    Answer: ____________________

26. 18 Question 18

    Solve 3^{x + 1} = 81.

    [2 marks]

    Answer: ____________________

27. 19 Question 19

    y is proportional to the square of x. y = 18 when x = 3. Find y when x = 5.

    [3 marks]

    Answer: ____________________

28. 20 Question 20

    Work out (4.2 × 10⁶) ÷ (1.5 × 10⁻³). Give your answer in standard form.

    [2 marks]

    Answer: ____________________

29. 21 Question 21

    From the top of a cliff 65 m high, the angle of depression of a boat is 28°. Find the distance from the foot of the cliff to the boat.

    [3 marks]

    Answer: ____________________

30. 22(a) Question 22(a)

    A circle has radius 10 cm. A chord is 12 cm long. Find the distance from the centre to the chord.

    [2 marks]

    Answer: ____________________

31. 22(b) Question 22(b)

    Two chords AB and CD meet at P inside a circle. AP = 4 cm, PB = 6 cm and CP = 3 cm. Find PD.

    [3 marks]

    Answer: ____________________

32. 23 Question 23

    Adult tickets cost $8 and child tickets cost $5. A cinema sold 4 times as many child tickets as adult tickets. It took $560. Form an equation and solve it to find how many of each ticket it sold.

    [4 marks]

    Answer: ____________________

33. 24 Question 24

    Plot the points (1, 2), (2, 4), (3, 5), (4, 4), (5, 7), (6, 8) on a scatter diagram, draw a line of best fit and describe the correlation.

    [3 marks]

34. 25 Question 25

    Find the equation of the tangent to the curve y = x² at the point where x = 3.

    [3 marks]

    Answer: ____________________

35. 26 Question 26

    A sector has radius 9 cm and arc length 3π cm. Find the angle of the sector.

    [3 marks]

    Answer: ____________________